A scalable parallel algorithm for three-dimensional semiconductor device simulation on unstructured tetrahedral meshes using drift-diffusion model is proposed,which is characterized by finite volume discretization,fully coupled Newton iterations for discretized nonlinear equations,and GMRES iterations using algebraic multigrid(AMG) preconditioner for linear equations in Newton iterations.The algorithm was implemented using a parallel adaptive finite element toolbox PHG.Large scale parallel numerical experiments with several problems,including PN diode and MOSFET,were carried out.In numerical simulations the largest mesh size are 500 million elements and the largest number of MPI processes used are 1 024.It shows that the proposed algorithm is efficient,robust and highly scalable.

This paper presents some preliminary work on the application of Schwarz alternating method, combined with a multigrid solver, for solving the steady 2D viscous incompressible Navier-Stokes equations. The difficulty caused by the violation of the compatibility condition imposed on the normal velocity at the boundary, which arises when subdomain problems are not solved exactly at each iteration, is surrounded by adding artificial compressiblity constants to the continuity equation each time when a subdomain problem is to be solved. These constants permit to maintain the compatibility condition of the subdomain problems and one can easily show that they tend to zero when the iteration number tends to infinity (in fact, they can be expressed explicitly as functions of the iteration number and some geometrical parameters of the computational domain). Numerical experiences have been made for flows in a channel with a facing step.